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National and Regional Contests
Iran Contests
Iran MO (2nd Round)
2003 Iran MO (2nd round)
1
Easy Inequality - Iran NMO 2003 (Second Round) - Problem4
Easy Inequality - Iran NMO 2003 (Second Round) - Problem4
Source:
October 4, 2010
inequalities
inequalities proposed
Problem Statement
Let
x
,
y
,
z
∈
R
x,y,z\in\mathbb{R}
x
,
y
,
z
∈
R
and
x
y
z
=
−
1
xyz=-1
x
yz
=
−
1
. Prove that:
x
4
+
y
4
+
z
4
+
3
(
x
+
y
+
z
)
≥
x
2
y
+
x
2
z
+
y
2
x
+
y
2
z
+
z
2
x
+
z
2
y
.
x^4+y^4+z^4+3(x+y+z)\geq\frac{x^2}{y}+\frac{x^2}{z}+\frac{y^2}{x}+\frac{y^2}{z}+\frac{z^2}{x}+\frac{z^2}{y}.
x
4
+
y
4
+
z
4
+
3
(
x
+
y
+
z
)
≥
y
x
2
+
z
x
2
+
x
y
2
+
z
y
2
+
x
z
2
+
y
z
2
.
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